The Montilla Knot: A Parametric Knotted Torus with Intrinsic Holonomy and Declared Topological Seam

We introduce the Montilla Knot, a closed parametric surface constructed by sweeping a periodic cross-section along the figure-eight knot (4₁) using a Bishop parallel-transport frame. The surface is defined by an explicit set of equations that guarantee closure of the cross-section and verified non-self-intersection. A key finding is that the figure-eight knot possesses an intrinsic holonomy angle of Theta = 31. 0694 degrees under parallel transport, which constitutes a topological invariant of the construction. Rather than concealing this geometric phase, we declare and characterize it as a formal property of the object, localizing the resulting seam at t = 0. We compute the Euclidean volume of the solid via Pappus's theorem and explicitly distinguish this from Thurston's hyperbolic volume of the knot complement. Potential applications include plasma confinement modeling, topological benchmarking of differential algorithms, and cosmological toy models of closed manifolds with geometric phase.